Summary
New developments in algorithms for density functional calculations within the Kohn-Sham methods allow to study systems with several hundreds of atoms. We present a linear scaling method for the construction of the Kohn-Sham Hamiltonian based on fast Fourier transforms. To solve the Kohn-Sham equation the orbital rotation method provides an efficient scheme for small to medium sized systems, where methods depending on the sparsity of the density matrix are not yet applicable. Combining these methods with multiscale algorithms will make it possible to access length and time scales relevant for many problems in materials science, life sciences or catalysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Berghold, M. Parrinello, and J. Hutter. Polarized atomic orbitals for linear scaling methods. J. Chem. Phys.116:1800, 1810, 2002.
C. Cavazzoni, G. L. Chiarotti, S. Scandalo, E. Tosatti, M. Bernasconi, and M. Parrinello. Superionic and metallic states of water and ammonia at giant planet conditions. Science283:44, 46, 1999.
R. Car and M. Parrinello. Unified Approach for Molecular Dynamics and Density-Functional Theory. Physical Review Letters55:2471, 2474, 1985.
CPMD V3.7 Copyright IBM Corp 1990-2003, Copyright MPI fur Festkorperforschung Stuttgart 1997-2001. see also www.cmpd.org.
P. Carloni and U. Rothlisberger. Simulations of enzymatic systems: Perspectives from Car-Parrinello molecular dynamics simulations. In L. Eriksson, editorTheoetical Biochemistry — Processes and Properties of Biological Systems, page 215. Elsevier Science, 2001.
J. R. Chelikowsky, N. Troullier, and Y. Saad. Finite-differencepseudopotential method — electronic-structure calculations without a basis. Phys. Rev. Lett.72:1240, 1243, 1994.
A. Edelman, T. A. Arias, and S. T. Smith. The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl.20:303, 353, 1998.
K. Eichkorn, O. Treutler, H. Ohm, M. Haser, and R. Ahlrichs. Auxiliary basis-sets to approximate coulomb potentials. Chem. Phys. Lett.240:283, 289, 1995.
L. Fusti-Molnar and P. Pulay. Accurate molecular integrals and energies using combined plane wave and Gaussian basis sets in molecular electronic structure theory. J. Chem. Phys.116:7795, 7805, 2002.
L. Fusti-Molnar and P. Pulay. The fourier transform coulomb method: E.cient and accurate calculation of the coulomb operator in a Gaussian basis. J. Chem. Phys.117:7827, 7835, 2002.
F. L. Gervasio, P. Carloni, and M. Parrinello. Electronic structure of wet DNA. Phys. Rev. Lett.89:1081022002.
C. K. Gan, P. D. Haynes, and M. C. Payne. First-principles densityfunctional calculations using localized spherical-wave basis sets. Phys. Rev. B63:2051092001.
S. Goedecker. Linear scaling electronic structure methods. Rev. Mod. Phys.71:1085, 1123, 1999.
E. Hern.andez, M. J. Gillan, and C. M. Goringe. Basis functions for linear-scaling first-principles calculations. Phys. Rev. B55:13485, 13493, 1997.
T. Helgaker, P. J. rgensen, and J. Olsen. Molecular Electronic-structure Theory. John Wiley & Sons Ltd, Chichester2000.
P. Hohenberg and W. Kohn. Inhomogeneous electron gas. Phys. Rev.136:B864, B871, 1964.
J. Hutter, M. Parrinello, and S. Vogel. Exponential transformation of molecular-orbitals. J. Chem. Phys.101:3862, 3865, 1994.
H. Horn, H. Weiss, M. Haser, M. Ehrig, and R. Ahlrichs. Prescreening of 2-electron integral derivatives in SCF gradient and hessian calculations. J. Comp. Chem.12:1058, 1064, 1991.
M. Krack and M. Parrinello. All-electron ab-initio molecular dynamics. Phys. Chem. Chem. Phys.2:2105, 2112, 2000.
W. Kohn and L. J. Sham. Self-consistent equations including exchange and correlation effects. Phys. Rev.140:A1133, A1139, 1965.
M. S. Lee and M. Head-Gordon. Polarized atomic orbitals for selfconsistent field electronic structure calculations. J. Chem. Phys.107:9085, 9095, 1997.
G. Lippert, J. Hutter, and M. Parrinello. A hybrid Gaussian and plane wave density functional scheme. Mol. Phys.92:477, 487, 1997.
G. Lippert, J. Hutter, and M. Parrinello. The Gaussian and augmentedplane-wave density functional method for ab initio molecular dynamics simulations. Theor. Chem. Acc.103:124, 140, 1999.
D. Marx and J. Hutter. ab-initio Molecular Dynamics: Theory and Implementation. In J. Grotendorst, editorModern Meth-ods and Algorithms of Quantum Chemistry, volume 1 of NIC Series, pages 329, 477. FZ Julich, Germany2000. see also www.fz-juelich.de/nic-series/Volume1.
P. Ordej.on, E. Artacho, and J. M. Soler. Self-consistent order-N density-functional calculations for very large systems. Phys. Rev. B53:R10441, R10444, 1996.
R. G. Parr and W. Yang. Density-Functional Theory of Atoms and Molecules. Oxford University Press, New York1989.
U. Rothlisberger. 15 years of Car-Parrinello simulations in physics,chemistry and biology. In J. Leszczynski, editorComputational Chemistry: Reviews of Current Trends, pages 33, 68. World Scientific, Singapore2001.
H. Sambe and R. H. Felton. New computational approach to slaters SCF-χa equation. J. Chem. Phys.62:1122, 1126, 1975.
J. VandeVondele and J. Hutter. An e.cient orbital transformation method for electronic structure calculations. J. Chem. Phys.118:4365, 4369, 2003.
T. Van Voorhis and M. Head-Gordon. A geometric approach to direct minimization. Mol. Phys.100:1713, 1721, 2002.
C. A. White, B. G. Johnson, P. M. W. Gill, and M. Head-Gordon. The continuous fast multipole method. Chem. Phys. Lett.230:8, 16, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hutter, J. (2004). Large Scale Density Functional Calculations. In: Attinger, S., Koumoutsakos, P. (eds) Multiscale Modelling and Simulation. Lecture Notes in Computational Science and Engineering, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18756-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-18756-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21180-8
Online ISBN: 978-3-642-18756-8
eBook Packages: Springer Book Archive